A Note on K-Theory of Azumaya Algebras |
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| Authors: | Roozbeh Hazrat Judith R Millar |
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| Institution: | 1. Department of Pure Mathematics , Queen's University , Belfast, Northern Ireland, United Kingdom r.hazart@qub.ac.uk;3. Department of Pure Mathematics , Queen's University , Belfast, Northern Ireland, United Kingdom |
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| Abstract: | For an Azumaya algebra A which is free over its centre R, we prove that K-theory of A is isomorphic to K-theory of R up to its rank torsions. We conclude that K i (A, ?/m) = K i (R, ?/m) for any m relatively prime to the rank and i ≥ 0. This covers, for example, K-theory of division algebras, K-theory of Azumaya algebras over semilocal rings, and K-theory of graded central simple algebras indexed by a totally ordered abelian group. |
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| Keywords: | Azumaya algebras K-Theory |
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